Department of Mathematics
Alfred P. Sloan Fellow
My research interests are in the area of mathematical biology, in particular, construction of mathematical models of biological systems within the framework of theories of continuum mechanics, dynamical systems, and stochastic dynamics.
DNA mechanicsMy current projects include the development micromechanical models of DNA elasticity that combine atomic-scale and continuum mechanics approaches with recent advances in computational chemistry and employ information obtained by X-ray crystallography, single-molecule manipulation, and other experimental techniques. Part of my research program is oriented towards continuum modeling of complex macromolecular assemblies and the application of stochastic and deterministic dynamics in the study of molecular biological processes.
Mathematical ImmunologyI am interested in the development of mathematical models of in-host human immune response to influenza A virus infection and the relation between immunity and inflammation. With my collaborators we have developed an ODE model for individual response, and an ensemble model capable of characterizing probabilistic outcomes of treatment scenarios.
Cell MigrationWe are developing a mathematical model of migration of enterocytes during intestinal wound healing process that is based on novel assumption of elastic deformation of the cell layer and incorporates cell mobility, adhesion and proliferation.
Math KangarooWith my colleague Piotr Hajlasz I organize a local testing site for Math Kangaroo, international mathematical competition for children grades 2-12. For more information see the link on the left or our article in Post-Gazette.